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Random walks on modular chains: Detecting structure through statistics.

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Kinetic transport in modular networks depends on global properties, not local structure. High-order moments reveal network details like inhomogeneity and repeating unit size, crucial for understanding charge transport.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Biophysics

Background:

  • Modular networks are crucial for understanding complex systems.
  • Kinetic transport phenomena are fundamental in various scientific disciplines.
  • Characterizing transport in heterogeneous systems remains a challenge.

Purpose of the Study:

  • To investigate kinetic transport in one-dimensional modular networks.
  • To determine how local and global network structures influence transport properties.
  • To explore the utility of high-order cumulants in revealing network architecture.

Main Methods:

  • Analytical modeling of kinetic transport.
  • Numerical simulations of transport dynamics.
  • Analysis of high-order cumulants (kurtosis, diffusion coefficient).

Main Results:

  • Mean transport velocity is insensitive to local network structure, depending only on global properties.
  • High-order cumulants (kurtosis, diffusion coefficient) reveal information about network inhomogeneity and repeating unit size.
  • The diffusion coefficient in biased chains weakly reveals structural motifs, with this dependence disappearing at low and high biasing.

Conclusions:

  • High-order moments of population distribution provide structural information beyond mean velocity.
  • These findings aid in deciphering mechanisms and architectures of long-range charge transport.
  • The study offers insights applicable to biomolecules and biological/chemical reaction networks.